Imported OBJ doesn't seem to render correct in object mode
It seems to me that it is like a clipping issue here:

Where can the viewport clipping parameters be changed?

But, for me it's more about scale. Normaly, objects fits in default clipping settings, but your is so huge! So I suggest you this:


Select all the staff, (it's looks like it is already selected) when press S,0,.,0,0,1,Enterto make it 100 times smaller (or even more if you want). 
When apply scale by pressing Ctrl+A -> Scale


Unfortunately import OBJ does not have scale option